POWER GENERATION AND TRANSMISSION
A given value of ns implies a given value of w, the peripheral coefficient, or ratio u -r- *\/2gh where u = peripheral speed of runner rim, feet per second, at the actual speed. Thus, for Allis-Chalmers reaction wheels:
Type A B C D E F G H
ns ............ 13.55 20.30 29.40 40.70 51.7-60.5 72.00 82 00 92.50
771 .... 0.585 0.625 0 665 0.70 0 75 0 80 0 77 0 815
If a wheel of type C were used under 400 ft. head at 1,200 r.p.m., the power developed at the runner would be (29.4 X 4005'4 -s- 1,200)2 = 1,920. With an efficiency of 0.80, the brake horsepower is 1,920 X 0.8 = 1,536. The volume of water required per second is Q = (550 X P)/62.4ft cu. ft., or 42.4 cu. ft. for the assumed conditions. The peripheral speed is 0.665 V2gh= 0-665 X 20 X 8.02 = 106.7feet per second and the wheel diameter is 106.7 X 12 -5- 207r= 20.4 in. Runners of high specific speed are usually less efficient at normal load than those of low specific speed, but hold up better in power and efficiency at over-gate flows, and are therefore best adapted for variable heads,
especially in low-head plants. The efficiency at part-load is of no importance unless water is stored, and storage in low-head plants is rare. High specific speeds imply large wheel diameters for a given head and rotative speed: the range of diameters (inches) being from l,070-\A/n to l,530\//i/7i for specific speeds from 13}-£ to 92J^-Since P = n«2. ft'^ -r n2, high specific speeds also increase the .power of a wheel to be operated at fixed head arid rotative speed.
Tangential (Impulse) Wheels.—The tangential water wheel is somewhat less efficient than the reaction turbine at full load, but its
FIG. 32.—Typical runner-blade profiles.
30 40 50
FIG 33.—Relations between characteristic speed, efficiency and gate-age of reaction turbines.
3 3.5 A 4.5 5 Characteristic Speed.
FIG. 34.—Relations between characteristic speed, efficiency and gateage of impulse wheels.
efficiency at underloads is relatively (and often absolutely) greater. The wheel diameter is usually about 840\/Ti -r n in., or is smaller for a given head and speed than that of a reaction wheel. The jet diameter is usually about >f2 the wheel diameter (Ho to Ho) and rarely exceeds 8 in. An approximate